Lens for Nikon crop body.

Just purchased a used D500 from a forum user (cheers Trev) and know bugger all about Nikon tbh. I bought it purely to use a big Sigma lens with but could really do with a couple of zooms to pack with it "just in case". I'm not after anything spectacular as I have my Pentax full frame body and lenses for landscape etc so after a bit of looking around the 24-120 f/4 and a 70-300mm of some description look favourite.

Are they reasonable lenses or can you recommend something else to cover this range ... also which 70-300mm should I be looking at?

Krispy and Kremey

The 24-70 f/4 is a decent performer with a good range of focal lengths and makes a great partner to a 70-300, especially the VR version. BUT, both are Fx lenses rather than Dx (although I believe there's a Dx 70-300) so relatively heavy. I'd look for a good copy of the 18-70 that was a kit lens with such bodies as the D70 and D200 - a kit lens because it came as part of many kits rather than because it's a "just about good enough" lens to keep people interested but make them look at a swift upgrade.

I'm a fan of the 18-70 too but if you have deeper pockets the 16-80 and older 16-85 are also worth a look. Not a lot wrong with the 18-140 either. 70-300 AF-P DX seems well regarded if you need something longer.

I have both the 24-120 f/4 and 70-300 VR lenses and aside from the 70-300 being a tad soft beyong 280mm I can't fault them. Mounted onto a D500 you will have a powerful set up which will also be ready for when/if you decide to go full frame.

A DX lens that is often derided, but which I found to be very good bvalue for money, is the 18-105 VR. Lightweight and compact with better than average optics

The only problem with 24-x is that it isn't that wide on DX. You could always supplement it with (e.g.) an 18-35 AFS FX if you need wider, of course. On the other hand, you can find the 18-70 DX for £60-80 and sell it for what you paid if you ever need FX. It's sharp and focuses fast and has a metal mount; its only real weakness is the level of distortion at the wide end, which you'll notice if you shoot architecture or other straight lines.

A 24-120 f/4 is a decent performer. Not as ultimately sharp as a Nikkor 24-70 f/2.8 but you'd be hard pushed to see much difference in real life. A Sigma 12-24 will cover the wide end at a reasonable cost but try before you buy, there are reports of dodgy copies WRT quality control.